Problem: Simplify. Remove all perfect squares from inside the square root. $\sqrt{56z^7}=$
Solution: Factor $56$ and find the greatest perfect square: $56=2\cdot 2\cdot 2\cdot 7=2^2\cdot 14$ Find the greatest perfect square in $z^7$ : $z^7=\left(z^3\right)^2\cdot z$ $\begin{aligned} \sqrt{56z^7}&=\sqrt{2^2\cdot 14\cdot \left(z^3\right)^2\cdot z} \\\\ &=\sqrt{2^2}\cdot \sqrt{14} \cdot \sqrt{\left(z^3\right)^2}\cdot \sqrt{z} \\\\ &=2\cdot \sqrt{14} \cdot z^3\cdot \sqrt{z} \\\\ &=2z^3\sqrt{14z} \end{aligned}$